Sic Bo

Last update: August 10, 2008

Sic Bo, meaning "dice pair" is an ancient Chinese gambling game. It is very popular in Macau, in my estimation second to only baccarat. In the United States is often found in the Asian gaming rooms, especially in Atlantic City. The large Las Vegas properties will usually have one table in the general casino.

The game uses three dice and a table with a variety of betting options on the roll of those dice. The odds and table layout may also vary from place to place. However, the payoffs are the same across Atlantic City and Macau, but different from each other. In Vegas and on the Internet casionos, anything is possible.

Image take from the Claridge Hotel/Casino rule book. Click on the image to see the rules on the next page.

Following is a list of the bets available. The payoffs vary on some bets, from casino to casino, so for those bets I indicte a range of viable payoffs.

Small: Wins on total of 4-10, except for a three of a kind. Probability of winning is 48.61%. Pays 1 to 1. House edge is 2.78%.
Big: Wins on total of 11-17, except for a three of a kind. Probability of winning is 48.61%. Pays 1 to 1. House edge is 2.78%.

Total of 4 and 17: Pays 50 to 1 in Macau, 60 to 1 in Atlantic City, and 62 to 1 in Australia.

House Edge for 4 and 17 Bets
Pays	Probability	Return
50	1.39%	29.17%
51	1.39%	27.78%
52	1.39%	26.39%
53	1.39%	25.00%
54	1.39%	23.61%
55	1.39%	22.22%
56	1.39%	20.83%
57	1.39%	19.44%
58	1.39%	18.06%
59	1.39%	16.67%
60	1.39%	15.28%
61	1.39%	13.89%
62	1.39%	12.5%
63	1.39%	11.11%
64	1.39%	9.72%
65	1.39%	8.33%

Total of 5 and 16: Pays 18 to 1 in Macau, 30 to 1 in Atlantic City, and 31 to 1 in Australia.

House Edge for 5 and 16 Bets
Pays	Probability	Return
18	2.78%	47.22%
19	2.78%	44.44%
20	2.78%	41.67%
21	2.78%	38.89%
22	2.78%	36.11%
23	2.78%	33.33%
24	2.78%	30.56%
25	2.78%	27.78%
26	2.78%	25%
27	2.78%	22.22%
28	2.78%	19.44%
29	2.78%	16.67%
30	2.78%	13.89%
31	2.78%	11.11%
32	2.78%	8.33%

Total of 6 and 15: Pays 14 to 1 in Macau, 17 to 1 in Atlantic City, and 18 to 1 in Australia.

House Edge for 6 and 15 Bets

Pays Probability Return

14 4.63% 30.56%

15 4.63% 25.93%

16 4.63% 21.3%

17 4.63% 16.67%

18 4.63% 12.04%

19 4.63% 7.41%
Total of 7 and 14: Pays 12 to 1 everywhere.

House Edge for 7 and 14 Bets

Pays Probability Return

10 6.94% 23.61%

11 6.94% 16.67%

12 6.94% 9.72%
Total of 8 and 13: Pays 8 to 1 everywhere.

House Edge for 8 and 13 Bets

Pays Probability Return

7 9.72% 22.22%

8 9.72% 12.50%
Total of 9 and 12: Pays 6 to 1 in Macau and Atlantic City. Pays 7 to 1 in Australia.

House Edge for 9 and 12 Bets

Pays Probability Return

6 11.57% 18.98%

7 11.57% 7.41%
Total of 10 and 11: Pays 6 to 1 everywhere. House edge of 12.50%.
Two-Number Combination: Bet on any of the 15 possible two dice combinations (for example a 1 and 2). Bet wins if both numbers appear. Probability of winning is 13.89%. Pays 5 to 1 in Atlantic City and Macau, for house edge of 16.67%. Pays 6 to 1 in Australia, for house edge of 2.78%.
Double: Bet on any specific pair (for example two 1's). Player wins if at least 2 of the number chosen appears. Pays 8 to 1 in Macau, 10 to 1 in Atlantic City, and 11 to 1 in Australia.

House Edge for Double Bets

Pays Probability Return

8 7.41% 33.33%

9 7.41% 25.93%

10 7.41% 18.52%

11 7.41% 11.11%

Triple: Player may bet on any specific trips (for example three 1's). Player wins if all 3 dice match the number chosen. Pays 150 to 1 in Macau and 180 to 1 in Atlantic City.

House Edge for Triple Bets
Pays	Probability	Return
150	0.46%	30.09%
155	0.46%	27.78%
160	0.46%	25.46%
165	0.46%	23.15%
170	0.46%	20.83%
175	0.46%	18.52%
180	0.46%	16.2%
185	0.46%	13.89%
190	0.46%	11.57%

Any Triple: Wins on any three of a kind. Pays 24 to 1 in Macau and 30 to 1 in Atlantic City.

House Edge for Any Triple Bet
Pays	Probability	Return
24	2.78%	30.56%
25	2.78%	27.78%
26	2.78%	25.00%
27	2.78%	22.22%
28	2.78%	19.44%
29	2.78%	16.67%
30	2.78%	13.89%
31	2.78%	11.11%
32	2.78%	8.33%

Any One Number: Bet on any specific number from 1 to 6. If chosen number appears 1 time bet pays 1 to 1, if it appears 2 times bet pays 2 to 1, and if it appears 3 times it pays 3 to 1 (in Atlantic City and Macau). Probability of 1 match is 34.72%, 2 matches is 6.94%, 3 matches is 0.46%. House edge of 7.87% (in Atlantic City and Macau). In Australia three matches pays 12 to 1, for a house edge of 3.70%.
Odd: Wins on any odd total, except loses with any three of a kind. This bet I have only seen in Macau, never in the United States. Probability of winning is 48.61% and house edge is 2.78%.

Even: Wins on any even total, except loses with any three of a kind. This bet I have only seen in Macau, never in the United States. Probability of winning is 48.61% and house edge is 2.78%.

Following are tables summarizing each bet under the Atlantic City and Macau rules.

Sic Bo — Atlantic City Rules
Bet	Pays	Winning Combinations	Probability	Return
Small, Big	1	105	0.486111	-0.027778
4, 17	60	3	0.013889	-0.152778
5, 16	30	6	0.027778	-0.138889
6, 15	17	10	0.046296	-0.166667
7, 14	12	15	0.069444	-0.097222
8, 13	8	21	0.097222	-0.125
9, 12	6	25	0.115741	-0.189815
10, 11	6	27	0.125000	-0.125000
Triple	180	1	0.004630	-0.162037
Any triple	30	6	0.027778	-0.138889
Double	10	16	0.074074	-0.185185
Two die combination	5	30	0.138889	-0.166667
Any number	1,2,3	75,15,1	0.421296	-0.078704

Following is a table summarizing each bet under the Macau rules.

Sic Bo — Macau Rules
Bet	Pays	Winning Combinations	Probability	Return
Small, Big	1	105	0.486111	-0.027778
Odd, Even	1	105	0.486111	-0.027778
4, 17	50	3	0.013889	-0.291667
5, 16	18	6	0.027778	-0.472222
6, 15	14	10	0.046296	-0.305556
7, 14	12	15	0.069444	-0.097222
8, 13	8	21	0.097222	-0.125000
9, 12	6	25	0.115741	-0.189815
10, 11	6	27	0.125000	-0.125
Triple	150	1	0.004630	-0.300926
Any triple	24	6	0.027778	-0.305556
Double	8	16	0.074074	-0.333333
Two die combination	5	30	0.138889	-0.166667
Any number	1,2,3	75,15,1	0.421296	-0.078704

Following is a table summarizing each bet under the Australia rules (source (PDF)).

Sic Bo — Australia Rules
Bet	Pays	Winning Combinations	Probability	Return
Small, Big	1	105	0.486111	-0.027778
4, 17	62	3	0.013889	-0.125000
5, 16	31	6	0.027778	-0.111111
6, 15	18	10	0.046296	-0.120370
7, 14	12	15	0.069444	-0.097222
8, 13	8	21	0.097222	-0.125000
9, 12	7	25	0.115741	-0.074074
10, 11	6	27	0.125000	-0.125000
Triple	180	1	0.004630	-0.162037
Any triple	31	6	0.027778	-0.111111
Double	11	16	0.074074	-0.111111
Two die combination	6	30	0.138889	-0.027778
Any number	1,2,12	75,15,1	0.421296	-0.037037

Sic Bo House Edge Comparison
Bet	Macau	Atlantic City	Australia
Small, Big	2.78%	2.78%	2.78%
4, 17	29.17%	15.28%	12.50%
5, 16	47.22%	13.89%	11.11%
6, 15	30.56%	16.67%	12.04%
7, 14	9.72%	9.72%	9.72%
8, 13	12.50%	12.50%	12.5%
9, 12	18.98%	18.98%	7.41%
10, 11	12.5%	12.50%	12.50%
Triple	30.09%	16.20%	16.20%
Any triple	30.56%	13.89%	11.11%
Double	33.33%	18.52%	11.11%
Two die combination	16.67%	16.67%	2.78%
Any number	7.87%	7.87%	3.7%

Yee Hah Hi

About 20% of the many Sic Bo tables in Macau use dice with pictures, instead of numbers. According to the Ultimate Casino Guide, by Michal Wiesenberg, the name of this game is "Yee Hah Hi." The translation is "Fish Shrimp Crab." Each picture has an associated number, as shown below. In addition to the usual bets there are some based on the colors of the symbols, as explained below.

Sic Bo — Chinese Dice Rules
Symbol	Color	Number
Fish	red	1
Scorpion	green	2
Goard	blue	3
Coin	blue	4
Crab	green	5
Rooster	red	6

All same color: Wins if all three dice are the same color. Pays 7 to 1. The probability of winning and house edge are both, coincidentally, 11.11%.

Excactly two of specific color: Wins if exactly two dice are a color chose by the player, for example red. Pays 3 to 1. The probability of winning is 22.22%, and house edge is 11.11%.

Excactly one of specific color: Wins if exactly one die is a color chose by the player, for example red. Pays 1 to 1. The probability of winning is 44.44%, and house edge is 11.11%.

Other Sic Bo sources:

Sic Bo appendix. This is a brief explanation of how the odds are calulated for each bet.
Mathematics of Sic Bo. This is an in-depth explanation of odds and probabilities in Sic Bo.

The Wizard's other sites: Wizard of Vegas, Wizard of Macau, Math Problems The Wizard recommends: The Bear Growls, Casinomeister, Online Casino Suite